Multiple pollutants, co-benefits, and suboptimal environmental policies

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Abstract

In our analytical general equilibrium model, polluting inputs can be substitutes or complements. We study a tax increase on one pollutant where the other faces a tax or permit policy. Our solutions highlight key parameters and welfare effects with gains from abatement plus positive or negative co-benefits from other pollutants in the covered and uncovered sectors. We demonstrate several ways taxes and permits differ. First, the change in taxed pollutant depends on whether the other pollutant faces a tax or permit policy. Also, only with a tax on the other pollutant can a co-benefit arise. The sign of co-benefits depends on the sign of cross-price elasticities and on whether the other pollutant's price is above or below marginal damages. Finally, the other pollutant's tax or permit policy also affects emissions in the uncovered sector (leakage). In a numerical illustration of carbon tax in U.S. electricity, we calculate emissions of CO2 and SO2 in both sectors. For plausible parameters, co-benefits are larger than direct

Introduction

In a multiple pollutant setting, the first-best can be achieved when each pollutant faces a tax or permit price that reflects its marginal environmental damage (Hanley et al., 2007, pp. 138–149). Not all pollutants are regulated, however, and even regulated ones likely face suboptimal policy. Thus, multiple pollutants create complications for regulators: tightening rules on one pollutant can affect emissions of other pollutants. Policymakers who adopt a new carbon policy may not be able to adjust each regulation on other types of pollution, especially where different laws and jurisdictions govern different pollutants. In fact, studies of a particular regulation may include “ancillary” co-benefits from reducing other pollutants (Burtraw et al., 2003, Groosman et al., 2011, Kolstad et al., 2014).

To consider the general problem of multiple pollutants, our simple analytical general equilibrium model has two sectors with competitive markets and constant returns to scale production functions. Our standard assumptions include full information, perfect factor mobility, and certainty, but a less standard assumption is that each sector has three inputs: a clean input and two kinds of pollution. With three inputs, any pair can be complements or substitutes. We refer to the clean input as labor, but it could represent labor, human capital, physical capital, or a composite of all clean inputs. For concreteness, our primary numerical example has one sector for electricity generation and another sector for the rest of the economy (including transportation), where both sectors use inputs of labor, sulfur dioxide (SO2), and carbon dioxide (CO2). Both pollutants in both sectors may face existing suboptimal policies, and then we consider a small increase in the tax on only one pollutant in one “covered” sector (e.g., carbon tax only in electricity generation). All equations are differentiated to linearize the model and to solve for the effects of that small policy change on all prices, quantities, and economic welfare.

The point of the general model is that raising a tax on one pollutant might increase or decrease the other pollutant. Thus, the model can encompass the example of Sigman (1996) who studies chlorinated solvents used for metal cleaning and degreasing; she finds that raised disposal costs for liquid chemical wastes leads to more air emissions. The empirical literature has many such examples.1 Regarding our specific numerical example for electricity generation, Färe et al. (2012) find that nitrogen oxides (NOX) and sulfur dioxide (SO2) are substitutes in production, but Agee et al. (2014) argue that CO2 and SO2 could be substitutes or complements.2 If they were substitutes, then a tax on CO2 could lead to more SO2, but the U.S. EPA assumes that a carbon tax reduces use of coal and therefore both CO2 and SO2 (i.e. complements). In this case, a carbon tax can have large positive co-benefits if it reduces damages from SO2.

Another complication, however, is that SO2 from power plants has been limited in the U.S. by a fixed number of permits under the Acid Rain Program (as studied by e.g., Schmalensee et al., 1998, Burtraw et al., 1998, Carlson et al. 2000). In this case, if a carbon tax changes demand for SO2, then permit prices may rise or fall depending on the degree of carbon and sulfur complementarity in production. But, if permits fix the quantity of SO2, then the carbon tax has no co-benefit from reducing sulfur emissions.

For these reasons, our general model allows each pollutant to face a pre-existing tax or permit price. Thus, we analyze four combinations. The case where both face a tax provides important baseline results showing the importance of cross-price substitution elasticities. We solve explicitly for the tax-tax and tax-permit scenarios, but the model is symmetric, so the permit-tax and permit-permit scenarios are analogous. Interestingly, we only need to consider the two pollutant policies in a “covered” sector (e.g., electricity generation), even though the other sector may also emit both types of pollution.

While some features of our model have appeared before, we obtain new results by combining all four of the following. First, we model analytically the general case where two pollutants can be complements or substitutes in production.3

Second, all pollutants need not be controlled by the same type of policy. While one pollutant might be subject to a tax, another is restricted by permits. Therefore, we use a framework that can analyze all combinations of tax or permit policies and allow for a relatively easy comparison of policy scenarios available to regulators.4

Third, these policies are likely not optimal; the price per unit of pollution does not equal marginal environmental damage. A pollutant's policy may not be optimal for at least three reasons: technical limitations and information constraints may preclude correct estimation of social costs and benefits; political concerns may prevent adoption of a first-best policy; and, a pollution tax would reflect conditions at the time of enactment rather than current conditions. Furthermore, multiple pollutants – even from a single source – may not have a single regulator using a comprehensive approach. We address situations where one regulator chooses a policy given regulations on other pollutants.5

Fourth, a pollution tax or permit system is unlikely to cover all sectors. The newly proposed Clean Power Plan applies only to the electricity generating sector, for example, just as did the Acid Rain Program of SO2 permits. A carbon tax might be able to cover more than just power plants, but it cannot cover all carbon emissions from small industry and residential sources (Metcalf and Weisbach, 2009). If it does not cover the entire economy, then a rise in the carbon price in the covered sector may have multiple second-best effects, as carbon emissions shift to uncovered sectors (i.e. carbon leakage).6

This combination of features in our analytical model allow us to show four ways that pollution taxes and permits differ, even with perfect certainty. First, for a tax increase on one pollutant, its quantity change depends on whether the other pollutant faces a tax or permit policy. At coal-fired power plants that face an increased carbon tax, even the carbon abatement itself depends on whether SO2 is taxed or permitted. Second, a raised carbon tax can increase or decrease SO2 emissions that face a tax, creating co-benefits that affect welfare, but not when SO2 faces a binding permit policy. Third, reductions in SO2 emissions may reduce welfare if that pollutant is already over-regulated in the covered sector with a tax above its marginal environmental damage. Fourth, whether that other pollutant in the covered sector faces a tax or permit policy also affects emissions of both carbon and sulfur in the uncovered sector, with additional impacts on welfare.

To illustrate these points, our numerical exercise uses data from 2007, one of the last years with binding U.S. regulation of SO2 emissions under the Acid Rain Program. In the tax-tax scenario, a 10% increase in carbon tax reduces CO2 by 4.3% and SO2 by 3.7%. However, the same carbon tax in the tax-permit scenario results in a much smaller decrease in CO2 emissions and zero change in SO2. Despite the same tax increase in both scenarios, welfare gains in the tax-tax scenario are almost twice the gains in the tax-permit scenario. Only in the tax-tax case can carbon policy yield co-benefits from SO2 reduction, and this co-benefit slightly exceeds the primary benefit under plausible parameters.

We note several important caveats. First, we emphasize that our simple analytical model cannot provide detailed or realistic predictions of effects of actual policy proposals. Instead, we intend only to study conceptual issues regarding interactions between sectors and between pollutants in general, when a tax on one can affect both pollutants and welfare in ways that depends on key parameters and on existing suboptimal policy. We insert values for parameters into our formulas only to illustrate the size of effects we study, not to compete with other detailed models.7

Second, for tractability, we collapse important dynamic effects into a simple static model. Carbon emissions cause complex future damages, but Nordhaus (2014) and others calculate the present value of costs from one ton of emissions today. Those future damages negatively affect the utility of infinitely lived individuals or of a dynasty where current generations care about their children. Also for tractability, we cannot capture the way SO2 damages vary by location, but we discuss likely effects. We assume both pollutants damages are separable in utility, but we discuss all of these caveats below.

Third, while we study tax policy and permit prices, we do not solve for effects of non-price policies like mandates or energy efficiency standards. Such standards can be studied in analytical general equilibrium models, but doing so here would add much complexity to this analysis. We point to Fullerton and Heutel (2010) and Goulder et al. (2016) for analytical general equilibrium models that incorporate mandates and compare them to price policies. To comply with a mandated reduction in emissions per unit of output, for example, firms can reduce emissions or increase output (or some of each). Thus it is equivalent to the combination of a tax on emissions with all revenue used to subsidize output. These issues are indeed interesting but are left to other papers.

Fourth, other papers study effects of a large policy change such as the introduction of an optimal carbon tax (e.g. $40/ton). For several reasons, however, we consider only small changes. First, our linearization is strictly valid only for small changes, and we can avoid the complexities of using two methodologies in one paper. Second, these small changes capture the fact that actual policy reform is most often incremental: policymakers make compromises and try out new policy ideas while avoiding major shocks to the economy. That is, the immediate adoption of a large carbon tax is unlikely. Third, our approach can still be used to analyze a large carbon tax, by considering a small change to a large pre-existing tax. Indeed, the U.S. already has restrictions on carbon, voluntary carbon markets, energy efficiency standards, and a gasoline tax. Those restrictions are represented in our simplified model by a pre-existing carbon tax. Finally, our small changes are conceptually useful to see all directions of change for each variable.

Section 2 below presents our basic model with multiple pollutants. Section 3 provides closed-form, analytical solutions for changes in endogenous variables, given an exogenous change in policy. Section 4 outlines our welfare analysis. Section 5 identifies plausible parameter values to calibrate the model. Section 6 uses those values for numerical results, and it conducts sensitivity analysis. Section 7 briefly concludes.

Section snippets

Model

As in other studies using linearization (e.g., Bovenberg and de Mooij, 1994; Fullerton and Metcalf, 2001), we assume perfect competition, full information, mobile factors, many identical agents, certainty, lump-sum transfers, costless enforcement of policies, and perfect mixing of pollutants (i.e. no “hot-spots”). While both sectors face a positive price for carbon emissions from various existing energy policies, we model effects of tightening carbon policy in a covered sector that does not

Analytical solutions for a change in carbon policy

Eqs. (1), (2), (3), (4), (5), (6), (7), (8), (9), (10) are the linear system for general equilibrium effects of a small policy change. Begin by applying the numeraire condition (p^L=0) and the assumption that pollution prices in sector X are fixed (p^CX=p^SX=0) to all remaining equations. Next, simplify Eq. (4) and compare it to Eq. (2) to show that p^X=0. Thus, good X acts as an equivalent numeraire, because all of its inputs have unchanged relative prices. Eq. (4) becomes redundant to Eq. (2)

Welfare changes

In general, changes in welfare depend on changes in all pollutants from all sectors. If a new policy targets one pollutant in one sector, it may have general equilibrium effects that increase or decrease other pollutants in the same sector or in other sectors. For concreteness, we look at CO2 policy in one sector that may affect SO2 emissions in that sector, or both CO2 and SO2 from the other sector. Since SO2 has environmental damages, one might think that its reduction would raise welfare,

Parameter values

This section provides parameter values for a numerical illustration that uses equations above to solve for endogenous outcomes and welfare. Analytical expressions in section 3 are complex, with some ambiguous signs, so this calculation can help evaluate both signs and magnitudes. The covered sector in this example is all of U.S. electricity generation, which emits both CO2 and SO2 and which can substitute away from carbon in the long run by switching from coal to natural gas, solar, or wind

Results with primary parameters

Our numerical results appear in Table 4. Column (1) reports results for the tax-tax policy scenario, where the carbon tax is increased by 10 percent, and an SO2 tax remains constant (so p^CY is 0.10 and p^SY is zero by assumption; those chosen entries are in bold). As a result of this policy change with primary-case parameters, covered CO2 emissions fall by 4.26 percent, and SO2 emissions fall by 3.65 percent. As the carbon price increases, complementarity between pollutants (eSC=3.6) leads to

Conclusion

To show expressions for all price and quantity outcomes in general equilibrium, this paper builds a two-sector, two-pollutant, analytical model of a closed economy using standard assumptions of perfect competition, constant returns to scale, mobile factors, and perfect certainty. The two pollutants in the covered sector may be complements or substitutes, where either might be controlled by a tax or by permits. We find closed-form solutions that show equilibrium outcomes for any parameter

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    We are grateful for suggestions from Stefan Ambec, Kathy Baylis, George Deltas, Firouz Gahvari, Garth Heutel, Stephen Holland, Jonathan Hughes, Ben Marx, Nick Muller, Till Requate, Ian Sue Wing, and anonymous referees. All mistakes are our own. Our email addresses are [email protected] and [email protected]. Mail can be sent to Fullerton at the Finance Department, University of Illinois at Urbana-Champaign, Champaign IL 61820 (phone is 512–750-6012).

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